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2000 AMC 10Problem 20P16-20~4 minPrint
Algebraic ManipulationAbsolute Value & InequalitiesApply an identity: SFFT, sum of squares, difference of cubes, VietaConsider the largest/smallest element or boundary case

Let AA , MM , and CC be nonnegative integers such that A+M+C=10A+M+C=10 . What is the maximum value of A⋅M⋅C+A⋅M+M⋅C+C⋅AA\cdot M\cdot C+A\cdot M+M\cdot C+C\cdot A ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.